2014/11/25 by Rainer Dyckerhoff, Dyckerhoff, Rainer, Pavlo Mozharovskyi +1 · 3 citations
Computer Science · Engineering · #Advanced Measurement and Metrology Techniques #Advanced Numerical Analysis Techniques #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Optical measurement and interference techniques
paper · doi:10.48550/arxiv.1411.6927
openalex publication_date 2014/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For computing the exact value of the halfspace depth of a point w.r.t. a data cloud of n points in arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole class of algorithms can be derived. In all of these algorithms the depth is calculated as the minimum over a finite number of depth values w.r.t. proper projections of the data cloud. Three variants of this class are studied in more detail. All of these algorithms are capable of dealing with data that are not in general position and even with data that contain ties. As is shown by simulations, all proposed algorithms prove to be very efficient.